To find whether the inverse of a function exists:
For a function to have an inverse it must be injective (one to one) - pass the vertical line test
It also must be strictly monotonous
1. Find the derivative of the function
2. Make the f'(x) = 0 , find all places where it is undefined or equal to 0
3 use the sign chart with the suspicious points. Plug in values near those points into the derivative function. if the sign changes then the function is not injective meaning that the inverse doesn't exist.
4. If the sign is constant throughout the function is strictly monotonous, hence the inverse exists.
For a function to have an inverse it must be injective (one to one) - pass the vertical line test
It also must be strictly monotonous
1. Find the derivative of the function
2. Make the f'(x) = 0 , find all places where it is undefined or equal to 0
3 use the sign chart with the suspicious points. Plug in values near those points into the derivative function. if the sign changes then the function is not injective meaning that the inverse doesn't exist.
4. If the sign is constant throughout the function is strictly monotonous, hence the inverse exists.
No comments:
Post a Comment